1. ## determinantQnine

find the determinant of the matrices below by inspection.give reson in each case.

B=
row1 2 7 -3 1
row2 0 3 7 4
row3 3 5 -12 1
row4 4 14 -6 2

C=
row1 a b c
row2 0 e f
row3 0 0 d

D=
row1 3 0 0
row2 0 -2 0
row3 0 0 -1

how to do it by inspection?

2. Dear mathseek,

by B look at the first and the 4th row.

C = a*e*d

3. ## determinantqnine

plse explain i don't get it !

4. Dear trythis, who are u?

statement:det(A) is surely 0 if one row is equal an other row multiplying by a number.

You can check the formula C = a*e*d easily with usage of determinant's definition.

D applys from C.

5. Originally Posted by mathseek
find the determinant of the matrices below by inspection.give reson in each case.

B=
row1 2 7 -3 1
row2 0 3 7 4
row3 3 5 -12 1
row4 4 14 -6 2
row 1 is 2 times row 4, hence matrix is singular do det =???

C=
row1 a b c
row2 0 e f
row3 0 0 d
Look at all those zeros, if you expand about the first column rather than the first row there is only one non-zero term.

D=
row1 3 0 0
row2 0 -2 0
row3 0 0 -1
same idea as for C

CB